2006/06/20 by V. Kaufman, Viktor Kaufman, Barbara Drossel +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Bioinformatics and Genomic Networks #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #cond-mat.dis-nn
paper · pdf · doi:10.1088/1367-2630/8/10/228
9 pages, 6 figures
arxiv created 2006/06/20 · openalex publication_date 2006/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Random Boolean networks (RBNs) were introduced in 1969 by Kauffman as a model for gene regulation. By combining analytical arguments and efficient numerical simulations, we evaluate the properties of relevant components of critical RBNs independently of update scheme. As known from previous study, the number of relevant components grows logarithmically with network size. We find that in most networks all relevant nodes with more than one relevant input sit in the same component, while all other relevant components are simple loops. As the proportion of nonfrozen nodes with two relevant inputs increases, the number of relevant components decreases and the size and complexity of the largest complex component grows. We evaluate the probability distribution of different types of complex components in an ensemble of networks and confirm that it becomes independent of network size in the limit of large network size. In this limit, we determine analytically the frequencies of occurrence of complex components with different topologies.